Notes on Hume's Treatise
by G. J. Mattey
Book I, Part II OF THE IDEAS OF SPACE AND TIME
§I. Of the infinite divisibility of our ideas of space and time
Hume gives an instance of the love of paradox by philosophers who use it to show their superiority over the vulgar and at the same time is eagerly received because it "causes surprise and admiration" which gives satisfaction to the mind. Such a paradox is the "doctrine of indivisibility," with whose examination the account of the ideas of space and time begins.
Everyone agrees (and it is evident from "the plainest observation and experience") that the capacity of the mind is limited and cannot reach a "full and adequate conception of infinity." But whatever can be divided infinitely contains an infinite number of parts: "'tis impossible to set any bounds to the number of parts without setting bounds at the same time to the division." So, thie idea of a finite quality is not infinitely divisible, but "by proper distinctions and separations we may this idea to inferio ones, which will be perfectly simple and indivisible." From the merely finite capacity of the mind follows an end in the division of ideas.
The minimum raised by the imagination cannot be sub-divided and cannot be reduced in size without being totally annihilated. We have ideas of numbers and proportions like the 1/1,000th or 1/10,000 part of a grain of sand, but the images of them are the same, and indeed the same as the image of the grain of sand itself. The idea of the grain of sand is not distinguishable into parts, and so is not separable into different ideas.
The same holds for impressions of sensation. A spot of ink held at a distance will suddenly vanish when removed even farther. This happens when the minimum is reached. A microscope or telescope "spreads" rays of light that flow from objects 1) gives parts to impressions [here he must mean bodies] that appear uncompounded to the naked eye, 2) makes what was imperceptible cross the threshold of the minimum.
Common opinion is in error when it thinks that the imagination cannot form an adequate idea of what is beyond a certain degree of smallness or largeness. We do form ideas of which nothing can be smaller, since they are minima. The "only defect of our senses" is the way they represent things as uncompounded when they really consist of parts. The mistake we make is in taking the impressions to be more or less equal in size to the objects they represent. Then we think that the fault is in the impressions, for not being able to represent any object smaller than these. But we can form ideas of things extremely small. The problem is getting a "just notion" of such a thing by enlarging our conceptions of it. Rival theories have even bigger problems, however. We can never have a just notion if the parts are infinitely divisible, and it is very difficult to get one if there are indivisible parts, since there are so many of them.